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Current time:0:00Total duration:3:12

Decomposing shapes to find area: subtract

CCSS.Math: ,

Video transcript

what is the area of the shaded figure so down here we have this green shaded figure and it looks like a rectangle except it has the square cut out in the middle so when we find its area we can think of it exactly like that we want to know how much space it covers it covers this rectangles amount of area with this square cut out so what we can do is find the area of the larger rectangle and then cut out or subtract the area of the square to see what's left in this shaded area so let's start by finding the area of this larger rectangle and to do that we can look at the side length it has a side side length of 9 and 8 to find area of a rectangle we can multiply the side length so 9 times 8 is 72 so that means that this rectangle covers 72 square centimeters this entire rectangular area cover 72 square centimeters but now we need to cut out or subtract the area of this square because that's not part of our shaded figure we need to cut that part out so to do that we know the side lengths are 4 on the square so we can think of this as this is 4 centimeters across so we can divide it into four equal sections and same going this way and then if we connect these lines what it will show us is that we have it's not drawn perfect but we have 4 rows of 4 square centimeters 4 times we see 4 square centimeters this top row 1 2 3 4 and so on 4 roast so there's 16 square centimeters we need to cut out of the 72 of this entire rectangular area we need to cut out or subtract sixteen of these square centimeters so let's do that we have 72 is the entire area and then let's start subtract out we subtract out ten of them just goes for me I like subtracting tens because they're simpler so for eight ten of the square centimeters now we're down to an area of sixty two left and then let's subtract those two more will get us to subtract two more will get us to sixty and then there's four left to subtract in order to subtract all sixteen so sixty minus four gets us to fifty six so the entire area of 72 we subtracted out these 16 square centimeters leaves us with a final area of fifty six square centimeters